A Link-Based Flow Model with Turn-Level Queue Transmission and Time-Varying Free-Flow Speed for Urban Road Networks

Abstract

Macroscopic link-based flow models are efficient for simulating flow propagation in urban road networks. Existing link-based flow models described traffic states of a link with two state variables of link inflow and outflow and assumed homogeneous traffic states within a whole link. Consequently, the turn-level queue length change within the link can not be captured, resulting in underrepresented queue spillback. Moreover, a constant link free-flow speed was assumed to formulate models, restricting their applicability in modeling phenomena involving time-varying free-flow speed. This study proposed a new link-based flow model by introducing an additional state variable of link queue inflow and adapting the link outflow to be free-flow speed-dependent. In our model, the vehicle propagation within each link is described by the link inflow, queue inflow, and outflow, which depends on the link free-flow speed changes. A node model is further defined to capture the presence of signal control and potential queue spillback, which estimates the constrained flow propagation between adjacent road segments. Simulation experiments were conducted on a single intersection and a network with consecutive intersections to verify the proposed model performance. Results demonstrate the predictive power of the proposed model in predicting traffic operations of intersections with multiple turning movements and time-varying free-flow speed. Our model outperforms the baseline link-based flow model and preserves the computational tractability property of link-based flow models.

Figures (25)

• Figure 1: Example of a road with turn lanes in the LQM, where the turn links can be created at a distance equal to the real directional lanes’ length.
• Figure 2: Illustration of the critical notations in the LQM, where $N_{i}^{in}$ is cumulative link inflow, $N_{i}^{qu}$ is cumulative queue inflow and $N_{i}^{out}$ is cumulative link outflow; $q_{i}^{in}$, $q_{i}^{qu}$ and $q_{i}^{out}$ are the link inflow rate, queue inflow rate and link outflow rate, respectively; $\rho_{q}$ is the queue density; $L_{i}$ is the link length; $L_f$ and $L_q$ are the lengths of queueing part and free-flowing part, respectively. Note that the time index $k$ is omitted from notations, but all the variables are time-dependent except $L_{i}$.
• Figure 3: Illustration of vehicle trajectories (top) and corresponding cumulative flow dynamics (bottom) at a certain sampling time step $k$ on a turn link, where $v_f(k)$ is the link free-flow speed at $k$; the flow dynamics include cumulative link inflow, cumulative queue inflow and cumulative link outflow that are determined by the proposed link model.
• Figure 4: Fundamental diagram for link $i$ at $k$, where the red curve represents the link in queueing states.
• Figure 5: Illustration of distance travelled by the entered flows on the link free-flowing part at different sampling time steps between $[k-4,k]$. (a) Fixed free-flow speed; (b) Time-varying free-flow speed.